Colonel Walter Kross, commander of the 436th Military Airlift Wing, formally established the Dover AFB Historical Center on October 13, 1986. Three days later, a Douglas C-47 Skytrain - the workhorse military transport of World War II - was airlifted from Muir Army Airfield in Pennsylvania to Dover. The museum grew across three hangars in the main area of the base through the early 1990s. The Air Force officially recognized it as a museum in 1995. The next year, the operation moved to Hangar 1301, a large hangar at the northwest corner of the base that had been built in the 1950s. In February 1997, the museum was renamed the Air Mobility Command Museum, reflecting the broader mission - to tell the history of the Air Transport Command, the Military Air Transport Service, the Military Airlift Command, and Air Mobility Command, the four organizations that had run the strategic airlift mission of the U.S. Air Force since the Second World War. The museum was closed to the public in 2001 for security reasons after the September 11 attacks and reopened in 2003 after a new access road allowed civilian visitors to reach the museum without crossing the secure base.

The collection's signature is its complete set of every significant Lockheed military airlifter used by the U.S. Air Force and Army since World War II. The Lockheed C-60 Lodestar, used in the war as a paratrooper transport. The Lockheed C-130E Hercules, the workhorse tactical transport that has been in continuous production longer than any military aircraft in history. The Lockheed C-141 Starlifter, both the A and B models - the long-range strategic jet transport that replaced the C-124 Globemaster II in the 1960s. The Lockheed C-5A Galaxy, the enormous strategic airlifter that flew tanks and helicopters across oceans. The C-5 in the collection is a particularly significant aircraft: it is one of the originals from the first production run. The Lockheed T-33 trainer rounds out the set. For the historian of American strategic airlift, the AMCM holds the most complete collection of the Lockheed line in the world. Lockheed's transport aircraft moved the U.S. military across a century of operations. The museum collects them as a single narrative.

Beyond the Lockheed set, the museum holds a remarkable collection of heavy military transport aircraft. The Douglas C-124A Globemaster II, with its huge clamshell nose, was the largest American transport when it entered service in 1950. The Douglas C-133B Cargomaster carried Atlas and Titan intercontinental ballistic missiles from manufacturing sites to launch complexes in the late 1950s and 1960s. The Douglas C-54M Skymaster was the long-range four-engine transport that flew the Berlin Airlift. The Fairchild C-119 Flying Boxcar and the Fairchild C-123K Provider represent the medium tactical transport gap between World War II piston aircraft and the C-130 jet era. The McDonnell Douglas C-9A Nightingale was the medical transport variant of the DC-9, designed specifically to evacuate wounded service members from forward areas. The KC-10 Extender, the McDonnell Douglas tanker built on the DC-10 airframe, was one of the most important air-refueling assets in U.S. service for forty years. Many of the aircraft are the first, last, or only examples of their model - the kind of provenance that aviation collectors rarely find in working condition.

The museum also holds the retired control tower cab from Dover AFB, which served the base from 1956 to 2009. The original tower stood 103 feet tall when it was operating. The cab now stands 39 feet at the museum, restored with its original 1960s-era radar consoles and radios. Visitors can climb up and see the view that air traffic controllers had as they directed C-141s and C-5s in and out of Dover for half a century. The fighter aircraft in the collection - the Convair F-106A Delta Dart, the McDonnell F-101B Voodoo - are not airlifters but represent the air-defense interceptor mission that protected the strategic airlift fleet from Cold War threats. The museum also holds a Bell UH-1N Iroquois - the Huey helicopter most famous from the Vietnam War. In September 2023, a new exhibit on Air Force Mortuary Affairs opened in conjunction with the work of the Charles C. Carson Center elsewhere on the base. The mortuary exhibit handles the most somber part of Dover's mission with the same care the AMCM brings to its aircraft restoration.

The Air Mobility Command Museum runs largely on volunteer labor. Active-duty Air Force personnel, retirees from the surrounding community, and aviation enthusiasts staff the museum's restoration shops, run the tours, and maintain the aircraft. The restoration program continues - many of the aircraft on display were brought in as derelicts and rebuilt at Dover over years of work. Admission is free, although donations are encouraged. The museum draws about 75,000 visitors a year, including thousands of school groups from across the Mid-Atlantic. The Education and Outreach Programs run STEM-related sessions on aerodynamics, propulsion, and aircraft systems. The museum is an unusual cultural institution: a working historical collection on an active military base, run by volunteers, free to the public, and producing aircraft that will be operational long after the original generation that flew them has gone. The B-17 that started the project, Shoo Shoo Shoo Baby, eventually did get delivered to the Air Force Museum in Dayton, but the people who restored it stayed at Dover. The museum's collection grew out of their dedication.